Perturbation Theory and Error Analysis.- Error bounds for the computation of null vectors with Applications to Markov Chains.- The influence of nonnormality on matrix computations.- Componentwise error analysis for stationary iterative methods.- The character of a finite Markov chain.- Gaussian elimination, perturbation theory, and Markov chains.- Iterative Methods.- Algorithms for periodic Markov chains.- Iterative methods for queueing networks with irregular state-spaces.- Analysis of p-cyclic iterations for Markov chains.- Iterative methods for finding the stationary vector for Markov chains.- Local convergence of (exact and inexact) iterative aggregation.- Queueing Theory and Applications.- Automated generation and analysis of Markov reward models using stochastic reward nets.- Means and variances in Markov reward systems.- A direct algorithm for computing the stationary distribution of a p-cyclic Markov chain.- Approximate analysis of a discrete-time queueing model of the shared buffer ATM switch.- Algorithms for infinite Markov chains with repeating columns.- Cray-2 memory organization and interprocessor memory contention.
This IMA Volume in Mathematics and its Applications LINEAR ALGEBRA, MARKOV CHAINS, AND QUEUEING MODELS is based on the proceedings of a workshop which was an integral part of the 1991-92 IMA program on "Applied Linear Algebra". We thank Carl Meyer and R.J. Plemmons for editing the proceedings. We also take this opportunity to thank the National Science Founda tion, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. xi PREFACE This volume contains some of the lectures given at the workshop Lin ear Algebra, Markov Chains, and Queueing Models held January 13-17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications. Markov chains and queueing models play an increasingly important role in the understanding of complex systems such as computer, communi cation, and transportation systems. Linear algebra is an indispensable tool in such research, and this volume collects a selection of important papers in this area. The articles contained herein are representative of the underlying purpose of the workshop, which was to bring together practitioners and re searchers from the areas of linear algebra, numerical analysis, and queueing theory who share a common interest of analyzing and solving finite state Markov chains. The papers in this volume are grouped into three major categories-perturbation theory and error analysis, iterative methods, and applications regarding queueing models.
This book presents recent research on Markov chains; the articles use linear algebra and queueing models and are grouped into three sections covering theory, models, and applications. This book will highlight current issues in the area and will be useful to both pure and applied mathematicians.